Time minimization and online synchronization for multi-agent systems under collaborative temporal logic tasks

Abstract

Multi-agent systems can be efficient when solving a team-wide task in a concurrent manner. However, without proper synchronization, the correctness of the combined behavior is hard to guarantee, such as to follow a specific ordering of subtasks or to perform a simultaneous collaboration. This work addresses the minimum-time task planning problem for multi-agent systems under complex global tasks stated as syntactically co-safe Linear Temporal Logic (sc-LTL) formulas. These tasks include the temporal and spatial requirements on both independent local actions and direct sub-team collaborations. The proposed solution is an anytime algorithm that combines the partial-ordering analysis of the underlying task automaton for task decomposition, and the branch and bound (BnB) search method for task assignment. We analyze the soundness, completeness and optimality regarding the minimal completion time. We show that a feasible and near-optimal solution is quickly reached while the search continues within the time budget. Furthermore, to handle fluctuations in task duration and agent failures during online execution, we propose an adaptation algorithm to synchronize execution status and re-assign unfinished subtasks dynamically to maintain correctness and optimality. Both algorithms are validated over systems of more than 10 agents via numerical simulations and hardware experiments, against several established baselines.